We designed the multireward arena (Fig. REF , left) to characterize emergent
swarming and reward approach behaviors, and the hairpin maze (Fig. REF ,
right) to assess behavioral adaptation in large, fragmented environments.
We observed several emergent dynamical behaviors in simulations of both
multi-agent swarming and single-entity locomotion (Section ,
Methods). The most notable and persistent behaviors included the emergence of
phase-sorted spatial formations such as line segments, rings, or concentric
loops (Fig. REF ). These behaviors were analogous in form to (1) the
`phase wave' states observed in certain swarmalator regimes [1]},
and (2) the hippocampal phenomena of theta sequences and theta-rhythmic phase
assemblies [2]}, [3]}. Further, by inspection of simulation
movies, we observed two dynamical features. First, agent subgroups forming line
segments and rings continuously phase-synchronized in a shared oscillation
that was independent from the absolute movement or rotation of the formation
in space. Second, line or ring formations would often break apart and re-form
new configurations that typically involved other agents or formations
that were able to phase-synchronize with elements of the subgroup. These
alternating disintegrative and aggregative dynamics may be consistent with
analyses of persistent homologies in place-cell networks with transient
connectivity [4]}.
